Gamma-ray burst (GRB) observations at very high energies (VHE; E > 100 GeV ) can impose tight constraints on some GRB emission models. Many GRB afterglow models predict a VHE component similar to that seen in blazars and plerions, in which the GRB spectral energy distribution has a double-peaked shape extending into the VHE regime. VHE emission coincident with delayed X-ray flare emission has also been predicted. GRB follow-up observations have had high priority in the observing program at the Whipple 10 m gamma-ray telescope, and GRBs will continue to be high-priority targets as the next-generation observatory, VERITAS, comes online. Upper limits on the VHE emission at late times (>~4 hr) from seven GRBs observed with the Whipple Telescope are reported here.